Title: Effect of sheared flow on magnetic islands

Abstract

The effect of sheared flow on a magnetic island is examined. In contrast to the density and temperature gradients which are flattened for sufficiently wide islands, it is found that the velocity gradient persists inside the separatrix whenever the constant-{psi} approximation is satisfied. It follows that velocity shear has a negligible effect on island amplitude in that approximation. The effect of the violation of the constant-{psi} approximation is explored by using the Kelvin-Stuart family of islands, and it is found that flattening is modest even when the separatrix encloses virtually all the current.

@article{osti_20974825,
title = {Effect of sheared flow on magnetic islands},
author = {Waelbroeck, F. L. and Fitzpatrick, R. and Grasso, Daniela and Burning Plasma Research Group, Department of Energetics, Politecnico di Torino and CNISM, C.so Duca degli Abruzzi 24, 10129 Turin},
abstractNote = {The effect of sheared flow on a magnetic island is examined. In contrast to the density and temperature gradients which are flattened for sufficiently wide islands, it is found that the velocity gradient persists inside the separatrix whenever the constant-{psi} approximation is satisfied. It follows that velocity shear has a negligible effect on island amplitude in that approximation. The effect of the violation of the constant-{psi} approximation is explored by using the Kelvin-Stuart family of islands, and it is found that flattening is modest even when the separatrix encloses virtually all the current.},
doi = {10.1063/1.2434251},
journal = {Physics of Plasmas},
number = 2,
volume = 14,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}

There is some experimental evidence that the E x B flows have radial structure that may be linked to rational surfaces. This flow structure may result from a self-organization process involving nonlinear flow amplification through Reynolds stress and fluctuation reduction by sheared flows. In stellarators, a large contribution to the Reynolds stress comes from the coupling of the magnetic field component of a vacuum field island with a plasma instability. In this process, the self-organization principle seems to be marginal stability for the fluctuations driving the flow.

The impact of sheared toroidal rotation on the evolution of pressure driven magnetic islands in tokamak plasmas is investigated using a resistive magnetohydrodynamics model augmented by a neoclassical Ohm's law. Particular attention is paid to the asymptotic matching data as the Mercier indices are altered in the presence of sheared flow. Analysis of the nonlinear island Grad-Shafranov equation shows that sheared flows tend to amplify the stabilizing pressure/curvature contribution to pressure driven islands in toroidal tokamaks relative to the island bootstrap current contribution. As such, sheared toroidal rotation tends to reduce saturated magnetic island widths.

The influence of local ExB flow shear on a relatively wide, constant-{psi}, magnetic island embedded in a large-aspect-ratio, low-{beta}, circular cross-section tokamak plasma is examined, using a slab approximation to model the magnetic geometry. It is found that there are three separate solution branches characterized by low, intermediate, and high values of the shear. Flow shear is found to have a stabilizing effect on island solutions lying on the low and high shear branches, via a nonlinear modification of the ion polarization term in the Rutherford island width evolution equation, but to have a destabilizing effect on solutions lying onmore » the intermediate shear branch. Moreover, the effect is independent of the sign of the shear. The modification of island stability by local ExB flow shear is found to peak when the magnitude of the shear is approximately v{sub i}/L{sub s}, where v{sub i} is the ion thermal velocity, and L{sub s} the magnetic shear length.« less

A systematic fluid theory of nonlinear drift-tearing magnetic island dynamics in a conventional large aspect-ratio low-{beta} circular cross-section tokamak plasma is derived from a set of single-helicity reduced neoclassical-magnetohydrodynamical equations which incorporate electron and ion diamagnetic flows, ion gyroviscosity, poloidal and toroidal flow damping, cross flux-surface momentum and particle transport, the sound wave, and the drift wave. The equations neglect the compressible Alfven wave, electron inertia, the electron viscosity tensor, magnetic field-line curvature, and finite ion orbit widths. A collisional closure is used for plasma dynamics parallel to the magnetic field. The influence of various different levels of flow dampingmore » on the phase velocity of an isolated island, as well as the ion polarization term appearing in its Rutherford equation, are investigated in detail. Furthermore, it is found that, under certain circumstances, a locked island is subject to destabilizing ion polarization term to which a comparable isolated (i.e., rotating) island is not.« less